Geological constituent estimation using calculated spectra relationships

ABSTRACT

A method for estimating at least one geological constituent may include obtaining a measured energy spectrum for the at least one geological constituent for a first borehole configuration, generating a calculated energy spectrum for the at least one geological constituent for the first borehole configuration, and generating a calculated energy spectrum for the at least one geological constituent for a second borehole configuration different than the first borehole configuration. The method may further include determining a relationship between the calculated energy spectra for the first and second borehole configurations, and generating an estimated energy spectrum for the at least one geological constituent for the second borehole configuration based upon the measured energy spectrum and the relationship between the calculated energy spectra for the first and second borehole configurations.

BACKGROUND

The decomposition of neutron-induced gamma ray spectra using full-energyreconstruction based on a linear combination of elemental standardspectra has been applied in many industries. Normally these elementalstandard spectra are measured in a controlled environment that may notbe representative of the environment to which they are applied. Anythingin the application environment that significantly alters the effects ofgamma ray scattering may make the elemental standards derived from themore simplistic environment inappropriate for the applicationenvironment. For example, changes in density have an impact on gamma rayscattering, and changes in hydrogen concentration may change thecharacteristic distribution of neutrons that defines the gamma raysource.

For oil well logging inside a borehole cased with a metal (e.g., steel)casing and/or cement, the additional gamma ray scattering from both themetal casing and cement reduces the total number of detected gamma rays.Moreover, this also changes the spectral character of the detected gammaray spectra since the effects of scattering are very dependent on theenergies of the gamma rays. It is possible to measure an energy spectrumfor a given geological constituent(s) in a reference (e.g., open-hole)environment, and then transform the measured spectrum to account for thechanges in scattering (e.g., from a casing, etc). However, toextrapolate such measurements to a different borehole environment (e.g.,a cased borehole) would ordinarily warrant using Monte Carlo modeling tofollow the entire history of each of the hundreds of gamma ray lines ofdifferent energies and intensities that contribute to the finalspectrum, which may not be practical or even possible in manyapplications.

SUMMARY

This summary is provided to introduce a selection of concepts that arefurther described below in the detailed description. This summary is notintended to identify key or essential features of the claimed subjectmatter, nor is it intended to be used as an aid in limiting the scope ofthe claimed subject matter.

A method for estimating at least one geological constituent may includeobtaining a measured energy spectrum for the at least one geologicalconstituent for a first borehole configuration, generating a calculatedenergy spectrum for the at least one geological constituent for thefirst borehole configuration, and generating a calculated energyspectrum for the at least one geological constituent for a secondborehole configuration different than the first borehole configuration.The method may further include determining a relationship between thecalculated energy spectra for the first and second boreholeconfigurations, and generating an estimated energy spectrum for the atleast one geological constituent for the second borehole configurationbased upon the measured energy spectrum and the relationship between thecalculated energy spectra for the first and second boreholeconfigurations.

A related apparatus is for estimating at least one geologicalconstituent and may include a processor and a memory cooperatingtherewith to obtain a measured energy spectrum for the at least onegeological constituent for a first borehole configuration, generate acalculated energy spectrum for the at least one geological constituentfor the first borehole configuration, and generate a calculated energyspectrum for the at least one geological constituent for a secondborehole configuration which is different than the first boreholeconfiguration. The processor and memory may further cooperate todetermine a relationship between the calculated energy spectra for thefirst and second borehole configurations, and generate an estimatedenergy spectrum for the at least one geological constituent for thesecond borehole configuration based upon the measured energy spectrumand the relationship between the calculated energy spectra for the firstand second borehole configurations.

A related non-transitory computer-readable medium may havecomputer-executable instructions for causing a computer to at leastobtain a measured energy spectrum for the at least one geologicalconstituent for a first borehole configuration, generate a calculatedenergy spectrum for the at least one geological constituent for thefirst borehole configuration, and generate a calculated energy spectrumfor the at least one geological constituent for a second boreholeconfiguration which is different than the first borehole configuration.Computer-executable instructions may also be provided to cause thecomputer to determine a relationship between the calculated energyspectra for the first and second borehole configurations, and generatean estimated energy spectrum for the at least one geological constituentfor the second borehole configuration based upon the measured energyspectrum and the relationship between the calculated energy spectra forthe first and second borehole configurations.

BRIEF DESCRIPTION OF THE DRAWINGS

The patent or application file contains at least one drawing executed incolor. Copies of this patent or patent application publication withcolor drawing(s) will be provided by the Office upon request and paymentof the necessary fee.

FIG. 1 is a schematic diagram, partially in block form, of a welllogging apparatus which may be used for estimating at least onegeological constituent in accordance with an example embodiment.

FIG. 2 is a flow diagram illustrating a method for estimating geologicalconstituents across different borehole configurations in accordance withan example embodiment.

FIG. 3 is a flow diagram illustrating a method for estimating geologicalconstituents in accordance with an example embodiment using full MonteCarlo calculations.

FIG. 4 is a graph of measured vs. calculated open-hole capture standardspectra for silicon.

FIG. 5 is a graph of cased-hole vs. open-hole calculated capturestandard spectra for silicon.

FIG. 6 is a graph of the ratio of cased-hole to open-hole capturestandard spectra for silicon.

FIG. 7 is a graph of the ratio of cased-hole to open-hole capturestandard spectra for titanium.

FIG. 8 is a graph illustrating the effects of casing thickness on theratio of cased to open-hole capture spectra for silicon.

FIG. 9 is a graph of a cased-hole silicon standard transformed from themeasured open-hole standard in accordance with an example embodiment.

FIG. 10 is a flow diagram illustrating a method for estimatinggeological constituents in accordance with an example embodiment usingscattering functions.

FIG. 11 is a graph of flux at the detector for mono-energetic gamma raysoriginating from the formation.

FIG. 12 is a graph in which the detector response is added to thescattering response functions from FIG. 11.

FIG. 13 is a graph in which the detector response and energy resolutionare added to the scattering response functions from FIG. 12.

FIG. 14 is a graph of relative full-energy propagation efficiency at thedetector for mono-energetic gamma rays originating from the formation.

FIG. 15 is a graph illustrating calculated capture standard spectra forsulfur from a high-density and a low-density formation.

FIG. 16 is a graph of the ratio between the calculated capture standardspectra from FIG. 15.

FIG. 17 is a graph of an example of a spectrum with nominal energyresolution, and one which has been transformed by the method illustratedin FIG. 3 to have improved resolution (e.g., narrower peaks).

FIG. 18 is a flow diagram illustrating a method for estimatinggeological constituents across different borehole tools in accordancewith an example embodiment.

DETAILED DESCRIPTION

The present description is made with reference to the accompanyingdrawings, in which example embodiments are shown. However, manydifferent embodiments may be used, and thus the description should notbe construed as limited to the embodiments set forth herein. Rather,these embodiments are provided so that this disclosure will be thoroughand complete. Like numbers refer to like elements throughout.

Referring initially to FIG. 1, a well logging system 30 is firstdescribed. A borehole 32 is drilled in a formation 31 with drillingequipment, and may use drilling fluid or mud. One or more portions ofthe borehole 32 may be lined with a casing 35, which may include metal(e.g., steel) cylindrical tubing, coiled tubing, cement, or both. Otherconfigurations may include: non-metallic casings such as fiberglass,high strength plastic, nano-material reinforced plastics etc; screens asused in some completions to prevent or reduce sanding; and slottedliners that may be used in completion of horizontal wells, for example.A logging device or tool 40 is suspended in the borehole 32 on anarmored multiconductor cable 33 to provide a wireline configuration,although other configurations such as logging while drilling (LWD),measurement while drilling (MWD), Slickline, coiled tubing orconfigurations such as logging while tripping may also be used. Thelength of the cable 33 substantially determines the depth of the device40 within the borehole 32. A depth gauge apparatus may be provided tomeasure cable displacement over a sheave wheel (not shown), and thus thedepth of logging device 40 in the borehole 32.

Control and communication circuitry 51 is shown at the surface of theformation 31, although portions thereof may be downhole. Also, arecorder 52 is also illustratively included for recording well-loggingdata, as well as a processor 50 for processing the data. However, one orboth of the recorder 52 and processor 50 may be remotely located fromthe well site. The processor 50 may be implemented using one or morecomputing devices with appropriate hardware (e.g., microprocessor, etc.)and non-transitory computer-readable medium components havingcomputer-readable instructions for performing the various operationsdescribed herein. It should also be noted that recorder 52 may also belocated in the tool, as may be the case in LWD tools, which may onlysend a certain amount of data to the surface while storing the bulk ofthe data in memory downhole to be read out at the surface after trippingout of the hole. In Slickline implementations there may be nocommunication with the surface, and data will be recorded and may beprocessed downhole for later retrieval and potentially furtherprocessing at the surface or a remote location.

The tool 40 may include one or more type of logging devices that takemeasurements from which formation characteristics may be determined. Forexample, the logging device may be an electrical type of logging device(including devices such as resistivity, induction, and electromagneticpropagation devices), a nuclear logging device, a sonic logging device,or a fluid sampling logging device, as well as combinations of these andother devices. Devices may be combined in a tool string and/or usedduring separate logging runs. Also, measurements may be taken duringdrilling, tripping, and/or sliding. Some examples of the types offormation characteristics that may be determined using these types ofdevices include the following: determination, from deepthree-dimensional electromagnetic measurements, of distance anddirection to faults or deposits such as salt domes or hydrocarbons;determination, from acoustic shear and/or compressional wave speedsand/or wave attenuations, of formation porosity, permeability, and/orlithology; determination of formation anisotropy from electromagneticand/or acoustic measurements; determination, from attenuation andfrequency of a rod or plate vibrating in a fluid, of formation fluidviscosity and/or density; determination, from resistivity and/or nuclearmagnetic resonance (NMR) measurements, of formation water saturationand/or permeability; determination, from count rates of gamma raysand/or neutrons at spaced detectors, of formation porosity and/ordensity; and determination, from electromagnetic, acoustic and/ornuclear measurements, of formation bed thickness.

Generally speaking, the present disclosure provides a reliable techniquefor transforming elemental standard spectra that have been carefullymeasured in a reference (e.g., open-hole) environment to elementalstandard spectra appropriate for another (e.g., cased-hole) environmentby accounting for the differences in gamma-ray scattering between thetwo environments. In an example embodiment, the measured open-holestandard spectrum for each element may be multiplied by the ratio ofcalculated (e.g., via Monte Carlo modeling) standards for that elementin the cased-hole and open-hole environments, respectively. An advantageof the approaches outlined herein are that they avoid the task ofmeasuring cased-hole elemental standard spectra for each casing sizethat might be encountered during oil field measurements, a task which isdifficult, time consuming, and the results of which are potentiallyinaccurate. The present approach provides for calculating the elementalstandard spectra based on Monte Carlo calculations of the gamma rayscattering response as a function of gamma ray energy. In addition tothe cased-hole application, this also can be used to transform elementalstandards to account for other environmental variation such as formationdensity, hole size, and other downhole conditions, as well as certaintool-to-tool variations. The techniques described herein may be usedwith various gamma-ray techniques and/or devices, including wireline orLWD tools, chemical or electronic source of neutrons, as well asinelastic or capture reactions. It should be noted that the approachesdescribed herein are not reserved to inelastic or capture reactions, asthey may also apply to gamma rays from activation and to natural gammarays or gamma rays emitted by radioactive contaminants in the ground.

By way of background, many different diameters and thicknesses of bothcasing and cement are encountered in oil wells. It would be possible,but not necessarily practical, to measure and extract elemental standardspectra for numerous combinations of casing and cement size that arelikely to be encountered. Moreover, the addition of casing and cement inlaboratory measurements of standards would notably complicate theextraction of the single-element spectral shapes, making it difficult ifnot impossible to arrive at a consistent set of elemental standardspectra across the range of casing and cement sizes. This lack ofconsistency in the elemental standards would directly affect theaccuracy of the final elemental concentrations from the spectralanalysis.

Rather than measuring a complete set of elemental standard spectra foreach unique environment, the approach set forth herein may be used withone or more sets of elemental standards that have been measured andextracted in one environment (e.g. open-hole), which may then betransformed or extrapolated to another environment (e.g., using MonteCarlo calculations) to quantify the differences in spectral shapebetween the different environments. It should be noted that the presentapproach may also be applied to improve open hole standards if suchstandard measurements are done in environments that are notrepresentative of or similar to the environment in which other standardmeasurements are taken. An example may be measuring a standard spectrumfor iron using an iron pipe surrounding the tool in a large water tank.Such spectrum is not entirely representative of an iron signal from irondistributed in a geological formation, however, for the purposes of thisdiscussion the term “geological formation” is used to cover suchelements in a geological environment or in such a stand-aloneimplementation. The transformation may be a ratio of the Monte Carlocalculated spectral shapes of each elemental standard for the differentenvironments. While Monte Carlo calculations of elemental spectra bythemselves may not be sufficiently accurate to replace the measuredspectra, the ratios of such Monte Carlo calculations may be sufficientlyaccurate to account for the environmental changes, thus allowing for thetransformation or extrapolation of the measured elemental spectra to adifferent borehole configuration or environment.

Referring initially to the flow diagram 60 of FIG. 2, beginning at Block61, an example approach for estimating one or more geologicalconstituents illustratively includes obtaining a measured energyspectrum for at least one geological constituent for a first boreholeconfiguration, at Block 62, generating a calculated energy spectrum forthe at least one geological constituent for the first boreholeconfiguration (Block 63), and generating a calculated energy spectrumfor the at least one geological constituent for a second boreholeconfiguration different than the first borehole configuration (Block64). By way of example, the first borehole configuration may be anopen-hole (uncased) borehole configuration, whereas the second boreholeconfiguration may be a cased or lined hole configuration (e.g., cementand/or steel casing, etc.). However, it should be noted that in someembodiments, the different borehole configurations could correspond todifferent factors besides casings or liners, such as different densityor porosity configurations, etc., as will be discussed further below.

The method further illustratively includes determining a relationship(e.g., a ratio) between the calculated energy spectra for the first andsecond borehole configurations, at Block 65, and generating an estimatedenergy spectrum for the at least one geological constituent for thesecond borehole configuration based upon the measured energy spectrumand the relationship between the calculated energy spectra for the firstand second borehole configurations, at Block 66. As will be appreciatedby those skilled in the art, the estimated energy spectrum may then beused to determine a relative amount (e.g., a percentage) of thegeological constituent(s) present adjacent to the second borehole, atBlock 67, by comparison with measured element spectra for variousconstituents in the formation. The method of FIG. 2 illustrativelyconcludes at Block 68.

Turning now to the flow diagram 70 of FIG. 3, an example embodiment fortransforming standard spectra using full Monte Carlo calculations is nowdescribed. In the present example, the first borehole configuration isan open borehole, and the second borehole configuration is a casedborehole. The flow diagram 70 summarizes an example approach fortransforming measured open-hole spectral standards using ratios of fullMonte Carlo calculated spectra. With reference to the graph 80 of FIG.4, it may be seen that the standard energy spectra plot 81 for siliconcalculated (e.g., via Monte Carlo modeling) matches the measuredstandard spectra plot 82 for silicon relatively closely. While thedifference between the two may be enough to avoid using the modeledcapture spectra in place of the measured spectra, it has been determinedthat this difference is close enough that the relationship betweencalculated spectra for open and cased-hole environments (or otherdifferent environments) may be used to transform or extrapolate themeasured spectra from the reference environment to a different boreholeenvironment. Beginning at Block 71, the elemental standard spectra forthe cased-hole and open-hole environments are respectively determined atBlocks 72, 73 using Monte Carlo calculations, although other suitablecalculation techniques may be used in different embodiments, as will beappreciated by those skilled in the art.

Adjustment parameters may be applied to the calculated spectra asappropriate, such as those of the detector system, including theenergy-to-channel calibration (e.g., the gain, offset, and linearity ofthe measurement system) and the energy dependence of the energyresolution. These parameters may then be applied to the Monte Carlocalculations for different elements in the various environments (Blocks74, 75), or after determining the above-noted ratio, for example.

More particularly, referring to the graph 85 of FIG. 5, Monte Carlocalculations of the silicon standard spectra 86, 87 in both open-holeand cased-hole environments, respectively, are shown. In this example, asteel casing 0.231 inches thick was used, along with a cement liner 0.50inches thick, although other casing or liner configurations ordimensions may be used in different embodiments. For comparisonpurposes, the spectra have been normalized to be equal at high energies.The calculations appear fairly similar above 3 MeV, but below this levelmore down-scattering is present in the cased-hole environment, as wellas more attenuation of the observable full-energy peaks.

Referring to the graph 90 of FIG. 6, a plot 91 of the ratio (determinedat Block 76) of cased-hole to open-hole Monte Carlo calculated standardspectra 87, 86 (from FIG. 5) for silicon for the above case of a0.231-inch casing and 0.50 inches of cement is illustrated, againnormalized at high energy. In the graph 95 of FIG. 7, a similar plot 96of the ratio for titanium is shown. These ratios are theenergy-dependent transformations that one may apply to the measuredopen-hole standard spectra for silicon and titanium (Block 77) toproduce elemental standards appropriate for this cased-hole environment.It will be appreciated that the transform (Block 78) is different foreach element, and thus a separate calculation for each element is used.The method of FIG. 3 illustratively concludes at Block 79.

Referring to the graph 100 of FIG. 8, the cased-hole to open-hole ratiosfor silicon calculated for four different steel casing thicknesses(namely 0.54 inches, 0.45 inches, 0.32 inches, and 0.23 inches, and allwith a cement thickness of 0.5 inches), show that it is desirable tocalculate the transform for each different environment to providedesired accuracy. With respect to applying the transform, the graph 105of FIG. 9 compares the measured open-hole silicon standard spectrum 106to the cased-hole silicon standard spectrum 107, which has beentransformed to be appropriate for the environment of 0.231 inch casingand 0.50 inch cement using the techniques described herein.

In the above-described approach, elemental standard spectra werecalculated using Monte Carlo calculations to track the entire history ofthe reactions from neutron production to gamma ray detection. While thistechnique may overall be the most accurate method available for mostmodeling applications, other approaches may also be suitable for certainapplications. For example, referring now to the flow diagram 110 of FIG.10, elemental standards calculations using gamma ray scatteringfunctions may have some advantages when applied to transformingelemental standard spectra for different environments.

Beginning at Block 111, the premise here is to decouple the Monte Carlocalculation of gamma ray scattering from the underlying emissionspectrum for a given element, at Block 112. This is possible because thescattering effects vary as a function of the logging environment, whilethe gamma ray production spectrum is a constant fundamentalcharacteristic for each element and neutron reaction. Gamma rayproduction cross sections for each element are generally known, as willbe appreciated by those skilled in the art. To model the scattering,Monte Carlo calculations may be used to generate a set of gamma ray“scattering functions” which represents the energy-dependent flux at thesurface of the detector that results when gamma rays of a single energyare produced in the formation (Blocks 113, 114). The detector-specificresponse to this incident flux may be calculated and optimized asbefore, and then folded into the scattering functions, at Blocks 115,116. The standard spectrum for each element may then be calculated as alinear combination of the appropriate scattering functions weighted bythe gamma ray production cross sections for that element for each gammaray energy.

Generation of these scattering functions may be as follows. Startingwith a characteristic spatial distribution of gamma rays produced in theformation, the Monte Carlo code may then track these gamma rays to thedetector. The graph 125 of FIG. 11 shows the result of this calculationfor four initial gamma ray energies at 2, 4, 6, and 8 MeV in thecased-hole environment with a casing thickness of 0.54 inches and cementthickness of 0.50 inches. These scattering functions should be availablefor an arbitrary energy, but because they vary so smoothly from oneinitial energy to the next, interpolation techniques based oncalculations of a relatively small number of different original gammaray energies may be used. This approach was tested with 110 gamma rayenergies in 100-keV increments, but far fewer would have producedresults of equivalent quality.

In the graph 130 of FIG. 12, part of the detector response has beenadded to the gamma ray scattering functions, showing the energydeposited in the detector system and not merely the flux striking thesurface of the detector due to the mono-energetic formation gamma rays.This detector response is determined in a separate Monte Carlocalculation, which may be specific to the material and size of thedetector being used for the measurements. Furthermore, in the graph 135of FIG. 13, the detector energy resolution is also added to thescattering functions. Other parameters of the energy-to-channelcalibration (e.g., gain, offset, nonlinearity) may also be matched tovarious measured spectra.

The result is the detector response for mono-energetic gamma raysoriginating in the formation, which may be interpolated for differentarbitrary original gamma ray energies. Using tabulated gamma rayproduction cross sections for each element, the elemental standardspectrum may then be calculated as a linear combination of theappropriate scattering functions weighted by the gamma ray productioncross sections for each gamma ray energy. As before, an energy-dependenttransform may be derived by taking the ratio of two calculated elementalstandards, namely one for the appropriate cased-hole environment and onefor the open-hole environment of the measured standard (Blocks 117-119).This spectral ratio may be multiplied by the measured open-holestandard, as discussed above. The method of FIG. 10 illustrativelyconcludes at Block 120.

Various advantages of the foregoing approach to estimating elementalstandard spectra will be appreciated. For example, because the gamma rayscattering functions are relatively “well behaved” (i.e., smoothlyvarying), it may be possible to predict them for an arbitraryenvironment based on a targeted number of environments used for theexplicit calculations. For example, the graph 140 of FIG. 14 shows therelative full energy propagation efficiency for several differentcased-hole environments. A parameterization of this quantity, possiblycombined with other environmentally dependent parameters, may be used togenerate scattering functions for a given combination of casing andcement geometry.

Furthermore, unlike using full Monte Carlo calculations for eachelemental standard, with this approach no statistical sampling has to beperformed for the gamma ray production cross sections. The emissionlines are a known constant, and the Monte Carlo simulation is devoted tothe effects of gamma ray scattering. This notably reduces thestatistical scatter when computing the spectral ratio for differentenvironments. This is illustrated by the regularity seen in FIG. 8,since the ratios here came from elemental standards calculated via thescattering function approach.

In addition, the best available gamma ray production cross sections foreach element may be used even though they might not have beenincorporated into the existing Monte Carlo code. Moreover, once thescattering functions have been calculated, the elemental standardspectra for any element for which gamma ray production cross sectionsare known may be calculated extremely quickly. The addition of newelemental standards to the spectral analysis may not warrant a new setof Monte Carlo calculations.

Despite such computational advantages, the scattering function approachmay be less accurate than using full Monte Carlo simulations of theelemental spectra. One notable advantage of the fully detailedsimulation is that it accounts for how the logging environment affectsthe transport and scattering of neutrons. The spatial distribution ofneutrons around the tool determines the shape of the gamma ray source inthe formation, borehole, and completion. While the scattering functionsin their simplest form use a constant spatial distribution of gamma raysin the formation, in reality the originating gamma ray distributiondepends on parameters including, but not limited to: formation hydrogenindex; formation density; borehole size; borehole fluid; and thegeometry of the casing and/or cement. A more detailed implementation ofthe scattering function method may take these parameters into account,such as by using a customized photon source distribution for eachcombination of borehole size and casing geometry, for example, as willbe appreciated by those skilled in the art.

As noted above, the transforms may be used for additional properties ofthe logging environment as well. While the derivation of cased-holestandard spectra may be the application of particular interest for theabove-described ratio-transformation approaches, the true shape of thespectrum for each element is affected by other properties of the loggingenvironment as well. This is true for properties of open-holeenvironments as well as the details of the completion in a cased-holeenvironment. Therefore, the approaches described herein have potentialapplications for transforming standard spectra, whether open-hole orcased-hole, based on other properties of the formation or borehole thataffect neutron and gamma ray scattering.

As one of many possible illustrative examples, a potential applicationwould be to transform open-hole standards based on formation density.For example, the graph 145 of FIG. 15 shows full Monte Carlocalculations of the sulfur capture spectrum from two formations: ahigh-density formation of 0-p.u. anhydrite at 2.97 g/cc, and alower-density formation of porous gypsum at 1.87 g/cc. The spectra arenormalized together at high energy. The graph 150 of FIG. 16 shows theratio of the two spectra. The spectral difference in this example is notas pronounced as in the previous cased-hole examples. However, the ratioin FIG. 16 shows that there is an energy-dependent difference that isneglected in an analysis with fixed spectral shapes.

A set of spectral ratios based on formation density at various intervalsmay be derived from full Monte Carlo calculations for each element, asin this example for sulfur. Also, the approach using scatteringfunctions may be developed here, using Monte Carlo to calculate thescattering behavior for mono-energetic gamma rays originating informations of various densities. Each approach has advantages anddisadvantages as discussed above, but this example indicates that theaccuracy of the full Monte Carlo calculation may be desirable forcapturing the subtle spectral differences seen in FIG. 15.

Of particular note is that the sulfur-from-anhydrite spectrum is lowerat low energy than that of the sulfur from the less dense gypsumformation, and its full-energy peaks are slightly more pronounced. Thisresult is counter-intuitive when considering just the effects of densityon gamma ray scattering, that is, high density causes more attenuationand scattering which should shift the spectrum toward low energy.However, these formations also have very different porosity and hydrogenindex, which affects the spatial distribution of neutrons. That is, thelow-porosity anhydrite allows more thermal energy neutrons close to thedetector, which reduces the distance that the resulting gamma rays haveto travel to be detected. Variation in liquid-filled porosity thereforecauses simultaneous changes in neutron and gamma ray transport thatpartially cancel one another in the final shape of the detectedspectrum. In contrast, a change in gas-filled porosity would have muchless effect on hydrogen index, and the neutron transport would exhibityet a different behavior when the density changes.

A more rigorous implementation of the full Monte Carlo approach would beto calculate ratio transforms that depend simultaneously on formationdensity and hydrogen index. By contrast, such effects may be included inan implementation of the scattering function approach, e.g., bycalculating density-dependent scattering functions in which the initialgamma ray distribution depends on hydrogen index. These interdependencesare more naturally coupled in the full Monte Carlo approach as shownhere. The skilled artisan will accordingly appreciate that theillustrative example may be repeated for many different physicalproperties of the logging environment or a combination thereof,including formation hydrogen index or porosity, formation density,borehole size, borehole fluid, positioning of the tool in the borehole,details of a cased-hole completion as previously discussed, etc.

In addition to applications based on the logging environment, theabove-described ratio transforms may also be used to addresstool-to-tool variation in spectral response. Normally, elementalstandard spectra are derived from laboratory measurements with a toolwhich is chosen for its good performance. Each tool has a slightlydifferent spectral response, and it is a routine part of the analysis tomake adjustments to the elemental standards to optimize them for thedownhole measurements by other tools. These adjustments include thespectral response parameters previously discussed, includingnonlinearity and the degradation of energy resolution. However, someaspects of tool-to-tool variation are more challenging to adjust for,and they may be good candidates for treatment with the method ofcalculated ratio transforms.

Referring to the flow diagram 260 of FIG. 18, beginning at Block 261, anexample approach for calibrating borehole tools is now described. Moreparticularly, the above-described “ratio of calculated standards”technique may be used for tool calibration with respect to detectorresponse, and it takes advantage of being able to adjust the detectorresponse in the calculations. This allows for detector calibration toaccount for (1) differences in peak-shape, and (2) differences in theposition of the escape peaks. That is, the shapes of energy peaks and/orthe separation between the full energy peak and escape peaks in aspectral response may be different in different detectors, e.g., as aresult of detector crystal differences, etc.

A measured energy spectrum for at least one geological constituent for afirst borehole tool may be obtained at Block 262, along with generatinga calculated energy spectrum for the at least one geological constituentfor the first borehole tool (Block 263), and generating a calculatedenergy spectrum for the at least one geological constituent for a secondborehole tool, which is different than the first borehole tool (Block264), as discussed above. Moreover, the method further illustrativelyincludes determining a relationship (e.g., a ratio) between thecalculated energy spectra for the first and second borehole tools, atBlock 265, and determining a calibration parameter (e.g., a differentpeak shape or peak separation) for the second borehole tool based uponthe measured energy spectrum and the relationship between the calculatedenergy spectra for the first and second borehole tools, at Block 266which illustratively concludes the method of FIG. 18 (Block 268).

For the peak shape calibration, the standards may be calculated byadding resolution degradation both with symmetric Gaussians and withasymmetric Gaussians, where the degree of asymmetry would be determinedfrom the difference in the H-peaks shapes in a water-tank calibration,for example. An advantage of this approach over performing a transformto a composite spectrum is that it handles each of the detected gammarays individually because they are known in the calculation.

There may be a similar advantage to using this technique for anescape-peak shift calibration. For example, using the above-notedcalculations it is straightforward to identify the escape peaks in thedetector response functions since they are for a single energy gamma rayand originally have no resolution degradation, as will be appreciated bythose skilled in the art. Thus, a new set of detector response functionsmay be created with all of the escape peaks shifted, including (ifnecessary) the double escapes, and this would then act on every detectedgamma ray.

A process flow for a calibration procedure in accordance with oneexample embodiment may be as follows:

-   -   1. Perform Monte Carlo calculations for elemental standard        spectra;    -   2. Add detector response for first tool (e.g., gain, offset,        nonlinearity, energy resolution, peak asymmetry, escape-peak        separation);    -   3. Add detector response for second tool (e.g., gain, offset,        nonlinearity, energy resolution, peak asymmetry, escape-peak        separation);    -   4. Compute the ratio of calculated elemental standard spectra        for second vs. first tools;    -   5. Transform elemental standards measured by first tool to        standards appropriate for second tool;    -   6. Use transformed standards to reconstruct a calibration        measurement made by the second tool; and    -   7. Test for desired fit, which if obtained concludes the        process, but if not different parameters are chosen for the        detector response of the second tool and the process reverts        back to step 3.

One example of a non-trivial transformation is to take an elementalstandard spectrum and improve its energy resolution. Normally, thestandards are measured with a tool that has among the best resolutionavailable so that other tools just have to degrade the resolution ofthose standards (e.g., by a relatively simple convolution with aGaussian distribution). Occasionally, however, downhole measurements aremade with better resolution than appears in the laboratory elementalstandards. There is no simple convolution operation to “reverse”resolution degradation. An advantage of the above-described ratiotransforms is that the elemental standards may be calculated withdifferent energy resolutions, whether via the approach of fully detailedMonte Carlo calculations or the approach of scattering functions. Tofind the appropriate ratio for transformation, one may calculate thestandard spectrum with the nominal energy resolution of the measured setof standards, and also with the better resolution of the newmeasurement.

The graph 160 of FIG. 17 shows an example of a capture silicon standardplot 161 with nominal energy resolution, and a plot 162 for a versionwhich has been transformed by such a ratio to have improved resolution.It is a relatively straightforward exercise to degrade the improvedspectrum with a traditional convolution and verify that the result isnearly equivalent to the original spectrum.

Another potential application of the above-described approaches relatesto the tool-to-tool variation of peak shapes, and more specifically howsome detector systems produce peaks that are slightly asymmetrical. Itmay be desirable to adapt the nominal set of elemental standard spectrato match the appropriate peak shape behavior for each tool, but this mayordinarily be a somewhat difficult operation. However, by calculatingone standard spectrum using the spectral response that corresponds tothe measured standards, and then calculating another spectrum with agreater degree of asymmetry, we can again produce a ratio that providesthe desired transformation, as will be appreciated by those skilled inthe art.

Many modifications and other embodiments will come to the mind of oneskilled in the art having the benefit of the teachings presented in theforegoing descriptions and the associated drawings. Therefore, it isunderstood that various modifications and embodiments are intended to beincluded within the scope of the appended claims.

That which is claimed is:
 1. A method for estimating at least one geological constituent comprising: obtaining a measured energy spectrum for the at least one geological constituent for a first borehole configuration; generating a calculated energy spectrum for the at least one geological constituent for the first borehole configuration; generating a calculated energy spectrum for the at least one geological constituent for a second borehole configuration different than the first borehole configuration; determining a relationship between the calculated energy spectra for the first and second borehole configurations; and generating an estimated energy spectrum for the at least one geological constituent for the second borehole configuration based upon the measured energy spectrum and the relationship between the calculated energy spectra for the first and second borehole configurations.
 2. The method of claim 1 wherein the relationship between the calculated energy spectra for the first and second borehole configurations comprises a ratio thereof.
 3. The method of claim 1 wherein generating the calculated energy spectra comprises calculating the energy spectra for the at least one geological constituent using Monte Carlo calculations of a gamma ray scattering response as a function of gamma ray energy for the first and second borehole configurations, respectively.
 4. The method of claim 3 wherein the Monte Carlo calculations are used to determine at least one monoenergentic gamma ray scattering response for the first and second borehole configurations.
 5. The method of claim 1 wherein the at least one geological constituent comprises a plurality thereof; and further comprising determining a relative amount of each geological constituent based upon respective estimated energy spectra for the second borehole configuration.
 6. The method of claim 1 further comprising adjusting the calculated energy spectra for the first and second borehole configurations based upon at least one detection system parameter.
 7. The method of claim 1 wherein the first borehole configuration comprises an open borehole configuration; and wherein the second borehole configuration comprises a cased borehole configuration.
 8. The method of claim 1 wherein generating the calculated energy spectra for the first and second borehole configurations comprises calculating energy-dependent flux from gamma rays of a given energy level for the first and second borehole configurations.
 9. The method of claim 1 wherein the first borehole configuration corresponds to a first borehole diameter, and the second borehole configuration corresponds to a second borehole diameter different than the first borehole diameter.
 10. The method of claim 1 wherein the first borehole configuration corresponds to a first geological formation density, and the second borehole configuration corresponds to a second geological formation density different than the first geological formation density.
 11. The method of claim 1 wherein the first borehole configuration corresponds to a first geological formation porosity, and the second borehole configuration corresponds to a second geological formation porosity different than the first geological formation porosity.
 12. The method of claim 1 wherein the first borehole configuration corresponds to a first borehole fluid configuration, and the second borehole configuration corresponds to a second borehole fluid configuration different than the first borehole fluid configuration.
 13. An apparatus for estimating at least one geological constituent comprising: a processor and a memory cooperating therewith to obtain a measured energy spectrum for the at least one geological constituent for a first borehole configuration, generate a calculated energy spectrum for the at least one geological constituent for the first borehole configuration, generate a calculated energy spectrum for the at least one geological constituent for a second borehole configuration different than the first borehole configuration, determine a relationship between the calculated energy spectra for the first and second borehole configurations, and generate an estimated energy spectrum for the at least one geological constituent for the second borehole configuration based upon the measured energy spectrum and the relationship between the calculated energy spectra for the first and second borehole configurations.
 14. The apparatus of claim 13 wherein the relationship between the calculated energy spectra for the first and second borehole configurations comprises a ratio thereof.
 15. The apparatus of claim 13 wherein the calculated energy spectra is generated by calculating the energy spectra for the at least one geological constituent using Monte Carlo calculations of a gamma ray scattering response as a function of gamma ray energy for the first and second borehole configurations, respectively.
 16. The apparatus of claim 13 wherein the at least one geological constituent comprises a plurality thereof; and wherein the processor further cooperates with the memory to determine a relative amount of each geological constituent based upon respective estimated energy spectra for the second borehole configuration.
 17. The apparatus of claim 13 wherein the processor further cooperates with the memory to adjust the calculated energy spectra for the first and second borehole configurations based upon at least one detection system parameter.
 18. The apparatus of claim 13 wherein the first borehole configuration comprises an open borehole configuration; and wherein the second borehole configuration comprises a cased borehole configuration.
 19. A non-transitory computer-readable medium having computer-executable instruction for causing a computer to at least: obtain a measured energy spectrum for the at least one geological constituent for a first borehole configuration; generate a calculated energy spectrum for the at least one geological constituent for the first borehole configuration; generate a calculated energy spectrum for the at least one geological constituent for a second borehole configuration different than the first borehole configuration; determine a relationship between the calculated energy spectra for the first and second borehole configurations; and generate an estimated energy spectrum for the at least one geological constituent for the second borehole configuration based upon the measured energy spectrum and the relationship between the calculated energy spectra for the first and second borehole configurations.
 20. The non-transitory computer-readable medium of claim 19 wherein the relationship between the calculated energy spectra for the first and second borehole configurations comprises a ratio thereof.
 21. The non-transitory computer-readable medium of claim 19 wherein the calculated energy spectra is generated by calculating the energy spectra for the at least one geological constituent using Monte Carlo calculations of a gamma ray scattering response as a function of gamma ray energy for the first and second borehole configurations, respectively.
 22. The non-transitory computer-readable medium of claim 19 wherein the at least one geological constituent comprises a plurality thereof; and further having computer-executable instructions for causing the computer to determine a relative amount of each geological constituent based upon respective estimated energy spectra for the second borehole configuration.
 23. The non-transitory computer-readable medium of claim 19 further having computer-executable instructions for causing the computer to adjust the calculated energy spectra for the first and second borehole configurations based upon at least one detection system parameter.
 24. The non-transitory computer-readable medium of claim 19 wherein the first borehole configuration comprises an open borehole configuration; and wherein the second borehole configuration comprises a cased borehole configuration. 